A rubberband has mass 8.5g. The spring constant is 13.0. The rubberband is pulled back 3.4 cm. What is the velocity when rubberband is let go?
To find the velocity of the rubber band when it is let go, we can use the law of conservation of energy.
The potential energy stored in the rubber band when it is pulled back is equal to the kinetic energy when it is released. Mathematically:
Potential Energy = Kinetic Energy
The potential energy stored in the rubber band is given by the formula:
Potential Energy = (1/2) * k * x^2
Where:
- k is the spring constant (given as 13.0)
- x is the displacement of the rubber band (given as 3.4 cm or 0.034 m)
Plugging in the values into the equation, we get:
Potential Energy = (1/2) * 13.0 * (0.034)^2
= 0.00746 J
Since the potential energy is equal to the kinetic energy when the rubber band is released, we have:
Potential Energy = Kinetic Energy
0.00746 J = (1/2) * m * v^2
Where:
- m is the mass of the rubber band (given as 8.5 g or 0.0085 kg)
- v is the velocity we want to find
Rearranging the equation to solve for v, we get:
v^2 = (2 * Potential Energy) / m
v = sqrt((2 * 0.00746) / 0.0085)
= 2.69 m/s
Therefore, the velocity of the rubber band when it is let go is approximately 2.69 m/s.